A generalized conservation law for main-chain polymer nematics

TL;DR

This paper investigates the complex conservation laws in main-chain polymer nematics, emphasizing the importance of correctly integrating vectorial and tensorial constraints influenced by chain backfolding for accurate mesoscopic modeling.

Contribution

It clarifies the relationship between vectorial and tensorial conservation laws and highlights the necessity of a unified penalty potential in free energy formulations.

Findings

Vectorial and tensorial conservation laws are not equivalent but interconnected.

Chain backfolding significantly influences the relative importance of these laws.

Proper implementation of these laws is crucial for consistent coarse-grained models.

Abstract

We explore the implications of the conservation law(s) and the corresponding "continuity equation(s)", resulting from the coupling between the positional and the orientational order in main-chain polymer nematics, by showing that the vectorial and tensorial forms of these equations are in general not equivalent and can not be reduced to one another, but neither are they disjoint alternatives. We analyze the relation between them and elucidate the fundamental role that the chain backfolding plays in the determination of their relative strength and importance. Finally, we show that the correct penalty potential in the effective free energy, implementing these conservation laws, should actually connect both the tensorial and the vectorial constraints. We show that the consequences of the polymer chains connectivity for their consistent mesoscopic description are thus not only highly non-trivial but that its proper implementation is absolutely crucial for a consistent coarse grained description of the main-chain polymer nematics.